How many iterations are required for iterative-lengthening search when step costs are drawing from a continuos range [ϵ, 1]?
In the title of the question, you write (emphasis mine):


  step costs are drawn from a continuous range $[\epsilon, 1]$


If step costs are drawn from that range, it means that every step has a cost of at least $\epsilon$, and at most $1$. This leads back to the case that described in the question that you already understand.



Note that the book (at least, the third edition of the book) does state in the question that $0 &lt; \epsilon &lt; 1$. Of course, the question would not make much sense in the first place if negative costs were allowed.